Later on the floor of Parliament, Mr Turnbull said the reference to a "final solution" on immigration was a "shocking insult" to the Jewish people. In Nazi Germany, the extermination of Jewish people throughout Europe was known as "the final solution to the Jewish question".

Opposition Leader Bill Shorten also branded Senator Anning's speech "racist" and described it as "repugnant and disgraceful".

"I do not like seeing majorities pick on minorities," he said. "That is not the Australian way."

One Nation leader Pauline Hanson - whose infamous maiden speech in 1996 was dubbed racist for warning the country was in danger of being "swamped by Asians" - also joined the widespread condemnation of Senator Anning on Wednesday, saying she was "appalled" by the speech.

She claimed it was written by a sacked staffer to Malcolm Roberts - the former One Nation senator replaced by Senator Anning - and was "straight from the Goebbels handbook for Nazi Germany".

Mathias Cormann shakes hands with Fraser Anning after his controversial first speech. A spokeswoman has said Senator Cormann was merely following protocol.Credit:Alex Ellinghausen

"We are a multi-racial society and I have always advocated you do not have to be white to be Australian," Senator Hanson said.

Other senators said they regretted shaking Senator Anning's hand following his first speech, as is general protocol. A visibly-shaken Derryn Hinch said it was "one of the most disgraceful, racist, homophobic, divisive, misogynist, spiteful, hateful speeches I've ever heard", and made him feel like he was "trapped in a Ku Klux Klan rally".

"I want to apologise to the Senate and the Australian people that after this vomitous poison last night ... I dutifully lined up here and shook this unworthy man's hand," Senator Hinch said. "I then went home and I washed my own."